In the past, boiler pressure has been controlled with a simple proportional control which determines the firing rate (FR) for that particular burner. This can be expressed by the equation of ##EQU1## Where the firing rate is defined as between 0 and +1, P.sub.Hi is the upper pressure setpoint for the control of the boiler, and P.sub.Lo is the lower pressure setpoint for the boiler. This arrangement will be graphically disclosed in the specification, but generally indicates that at a low pressure in a typical boiler, the firing rate is very high. As the pressure increases, the firing rate is modulated down to what is referred to as a low fire position. The low fire position typically is the lowest safe operating point for the particular fuel burner arrangement.
There are two drawbacks to this type of a control. First is the fact that the greatest firing potential is available under very light load conditions, that is when the firing rate is at a minimum, and a second is the fact that as the P.sub.Hi and P.sub.Lo approach each other, the system becomes progressively less stable. It is not possible to have a single pressure setpoint with P.sub.Hi equal to P.sub.Lo with this type of a scheme. This general problem was addressed in the U.S. Pat. No. 4,373,663 which issued Feb. 15, 1985 in the name of Jeffrey M. Hammer, and is assigned to the assignee of the present application.
The Hammer patent addresses this problem in control of the pressure in a boiler by incorporating both a proportional and integral control functions. This can be expressed mathematically as ##EQU2## where E(t)=P.sub.Set -P(t) where P(t)=actual pressure at any time (t)
where P.sub.Set =pressure setpoint PA1 where K.sub.1, K.sub.2 are constants PA1 where .sub..DELTA. t =a unit of time.
The first term of the firing rate formula thus disclosed is comparable to the Hammer arrangement and is similar to a simple proportional control of a boiler. The second term is an integration of the past load history which is used to determine the present load. In order for this control method to be stable, the second term, that is the integral term, must be weighted much heavier than the first or proportional term. This scheme does not allow for a quick response to a step function or fast change in the actual load.